5. 3.2 Equations of Kinematics in Two Dimensions The x part of the motion occurs exactly as it would if the y part did not occur at all, and vice versa.
6. 3.2 Equations of Kinematics in Two Dimensions Example 1 A Moving Spacecraft In the x direction, the spacecraft has an initial velocity component of +22 m/s and an acceleration of +24 m/s 2 . In the y direction, the analogous quantities are +14 m/s and an acceleration of +12 m/s 2 . Find (a) x and v x , (b) y and v y , and (c) the final velocity of the spacecraft at time 7.0 s.
7. 3.2 Equations of Kinematics in Two Dimensions Example 1 A Moving Spacecraft In the x direction, the spacecraft has an initial velocity component of +22 m/s and an acceleration of +24 m/s 2 . In the y direction, the analogous quantities are +14 m/s and an acceleration of +12 m/s 2 . Find (a) x and v x , (b) y and v y , and (c) the final velocity of the spacecraft at time 7.0 s. x a x v x v ox t ? +24.0 m/s 2 ? +22 m/s 7.0 s y a y v y v oy t ? +12.0 m/s 2 ? +14 m/s 7.0 s
8. 3.2 Equations of Kinematics in Two Dimensions x a x v x v ox t ? +24.0 m/s 2 ? +22 m/s 7.0 s
9. 3.2 Equations of Kinematics in Two Dimensions y a y v y v oy t ? +12.0 m/s 2 ? +14 m/s 7.0 s
11. 3.3 Projectile Motion Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80m/s 2 .
12. 3.3 Projectile Motion Example 3 A Falling Care Package The airplane is moving horizontally with a constant velocity of +115 m/s at an altitude of 1050m. Determine the time required for the care package to hit the ground.
13. 3.3 Projectile Motion y a y v y v oy t -1050 m -9.80 m/s 2 0 m/s ?
14. 3.3 Projectile Motion y a y v y v oy t -1050 m -9.80 m/s 2 0 m/s ?
15. 3.3 Projectile Motion Example 4 The Velocity of the Care Package What are the magnitude and direction of the final velocity of the care package?
16. 3.3 Projectile Motion y a y v y v oy t -1050 m -9.80 m/s 2 ? 0 m/s 14.6 s
17. 3.3 Projectile Motion y a y v y v oy t -1050 m -9.80 m/s 2 ? 0 m/s 14.6 s
18. 3.3 Projectile Motion Conceptual Example 5 I Shot a Bullet into the Air... Suppose you are driving a convertible with the top down. The car is moving to the right at constant velocity. You point a rifle straight up into the air and fire it. In the absence of air resistance, where would the bullet land – behind you, ahead of you, or in the barrel of the rifle?
19. 3.3 Projectile Motion Example 6 The Height of a Kickoff A placekicker kicks a football at and angle of 40.0 degrees and the initial speed of the ball is 22 m/s. Ignoring air resistance, determine the maximum height that the ball attains.
21. 3.3 Projectile Motion y a y v y v oy t ? -9.80 m/s 2 0 14 m/s
22. 3.3 Projectile Motion y a y v y v oy t ? -9.80 m/s 2 0 14 m/s
23. 3.3 Projectile Motion Example 7 The Time of Flight of a Kickoff What is the time of flight between kickoff and landing?
24. 3.3 Projectile Motion y a y v y v oy t 0 -9.80 m/s 2 14 m/s ?
25. 3.3 Projectile Motion y a y v y v oy t 0 -9.80 m/s 2 14 m/s ?
26. 3.3 Projectile Motion Example 8 The Range of a Kickoff Calculate the range R of the projectile.
27. 3.3 Projectile Motion Conceptual Example 10 Two Ways to Throw a Stone From the top of a cliff, a person throws two stones. The stones have identical initial speeds, but stone 1 is thrown downward at some angle above the horizontal and stone 2 is thrown at the same angle below the horizontal. Neglecting air resistance, which stone, if either, strikes the water with greater velocity?
